Journal
MATHEMATICS
Volume 11, Issue 16, Pages -Publisher
MDPI
DOI: 10.3390/math11163487
Keywords
graph coloring; chromatic number; P-3-coloring; P-3-chromatic number; bipartite graphs
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The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P-3-coloring, was introduced. The aim of this article is to determine the P-3-chromatic number of different well-known classes of bipartite graphs and present algorithms to produce a P-3-coloring of these classes with a minimum number of colors required.
The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P-3-coloring, was introduced. A simple graph is called a P-3-colorable graph if its vertices can be colored so that all the vertices in each P-3 path of the graph have different colors; this is called the P-3-coloring of the graph. The minimum number of colors required to form a P-3-coloring of a graph is called the P-3-chromatic number of the graph. The aim of this article is to determine the P-3-chromatic number of different well-known classes of bipartite graphs such as complete bipartite graphs, tree graphs, grid graphs, and some special types of bipartite graphs. Moreover, we have also presented some algorithms to produce a P-3-coloring of these classes with a minimum number of colors required.
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